Rationality problem for norm one tori of tensor products of étale algebras and Hasse norm principle

Mathieu Florence, Akinari Hoshi, Aiichi Yamasaki

Let $k$ be a field. Let $A={\prod }_{i=1}^r{K}_i$ and $B={\prod }_{j=1}^s{E}_j$ be étale $k$-algebras where $K_i$ and $E_j$ are finite separable field extensions of $k$ with $[K_i:k]=m_i$…